# How does negative energy from Hawking Radiation cause a Black Hole to shrink? [duplicate]

Hello this is expanding upon a question that was previously asked on stack exchange that I linked below. From what I understand of Black Holes is that overtime Hawking Radiation results in the Black Hole shrinking. This being do to virtual particle pairs. The point I find confusing, and I may be misunderstanding it, but the black shrinks due to negative energy of the particle it absorbs when the other particle escapes but it does not matter whether or not it was the matter of the antimatter that was absorbed. Is the Black Hole losing mass if it absorbs only the normal matter half of a virtual particle and the antimatter half escapes?

Why does Hawking radiation cause black holes to die?

• possible duplicate of Black holes and positive/negative-energy particles – John Rennie Apr 5 '14 at 8:49
• Hello thank you for posting this but it does not quite ask or answer the question I posted. Main point I am confused on is how the Black Hole can shrink as a result of absorbing a particle due to the particle having negative energy even if the particle in question is an antiparticle through Hawking radiation? – John Apr 5 '14 at 17:12
• In GR all matter is treated as energy via Einstein's famous equation $e = mc^2$. GR makes no distinction between matter and energy - both create a gravitational field. Both matter and anti-matter have the same (positive) energy simply given by their mass. A negative energy particle is one that, in effect, has a negative mass, and of course adding a negative mass to a black hole will reduce its total mass. This is a gruesome oversimplification, but if you insist on using the particle-antip[article explanation of Hawking radiation this is basically what happens. – John Rennie Apr 5 '14 at 18:15
• Thank you, I miss-wrote part of the above question, I meant to say particle not antiparticle. Does the black hole still shrinks if it absorbs a normal particle and how? – John Apr 5 '14 at 19:54
• Both virtual particles and antiparticles may have a negative energy or a positive energy. Any negative energy object absorbed by the black hole will cause it to shrink because it decreases the total energy, and therefore mass, of the black hole. – John Rennie Apr 6 '14 at 6:03

the black hole shrinks due to negative energy of the particle it absorbs when the other particle escapes but it does not matter whether or not it was the matter of the antimatter that was absorbed.

For a virtual pair to become real particles, lets take an e+e- pair, energy must be provided by an energy source. In the simple pair creation by a real gamma ray hitting the field of a nucleus, the energy for the creation of e+e- is provided by the real gamma ray while the virtual from the field of the nucleus balances momentum .

In the case of the black hole the virtual pairs must get the energy from the great potential well that the BH is . When the random quantum mechanical fluctuations at the BH horizon give enough energy for the materialization of an electron or positron and enough energy that it escapes the hole, the energy comes from the potential well of the hole. This energy must be subtracted, that is why it is called negative, from the total potential to keep energy conservation at the horizon locally.

Is the Black Hole losing mass if it absorbs only the normal matter half of a virtual particle and the antimatter half escapes?

The electron and the positron have the same mass, positive, same is true for all particles antiparticles. As in relativistic energies E=mc^**2 it makes no difference if it is a particle or antiparticle that becomes real, energy will be subtracted from the total of the BH.

• So do evaporating black holes generate large quantities of anti-matter? – tvanc Feb 6 '16 at 9:45
• @turibe No, the numbers statistically of matter and antimatter would be equal but when one does the calculations the evaporation is very very slow , "Moreover, quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is on the order of billionths of a kelvin for black holes of stellar mass, making it essentially impossible to observe." these energies are not enough to create e+e-. en.wikipedia.org/wiki/Black_hole – anna v Feb 6 '16 at 10:50
• What about a small black hole, say one on the scale of those proposed for the scifi concept of using Hawking radiation for propulsion? Wouldnt those be evaporating more quickly and therefore releasing more energy? – tvanc Feb 6 '16 at 11:05
• @turibe have a look en.wikipedia.org/wiki/Micro_black_hole .. Hypothetical but maybe possible. – anna v Feb 6 '16 at 11:27